Background

In 1905, Einstein published a paper1 which laid the basis for special relativity. In that paper he derived special relativity’s time dilation equation, T=To(1−v2c2){\displaystyle T={\frac {T_{o}}{\sqrt {(1-{\frac {v^{2}}{c^{2}}})}}}}. It correlates time accumulating on a clock at rest in an inertial frame with another clock in a different inertial frame. In the above equation, v is the relative velocity between the two clocks.

Physics Meaning(s)

Special relativity’s time dilation is a function of relative velocity which requires that the time dilation effect of Clock A relative to Clock B has to be identical to the time dilation effect of Clock B relative to Clock A since the relative velocity between A and B is equal to the relative velocity between B and A. Hence, the initial reaction, circa 1905 -1916, from physicists was that special relativity’s time dilation described a “just observed” effect much like in optics when twins start together and, as they separate and the distance between them increases, each observes the other as shrinking, but, of course, no physical shrinking is actually occurring.

However, after deriving special relativity’s time dilation, Einstein, in that 1905 paper, made an assertion that caused great disagreement among physicists of that era. Einstein claimed that “From this …” [1] (clearly referencing time dilation) it followed that if two clocks were at rest together in an inertial frame and then one clock made a round trip away from and back to the other clock, then the “traveling” clock would have accumulated less proper time than the “stationary” clock. This assertion implied that special relativity’s time dilation caused the traveling clock to slow as a function of the relative velocity between the “stay-at-home” clock and the “traveling” clock. At the time, many physicists objected as it seemed contradictory to contend that an inherently symmetric effect would cause an inherently asymmetric physical effect. The resulting controversy was labeled the Clock Paradox and then in 1911 when Langevin [2] discussed it in terms of the relative aging of twin humans, it became known as the Twin Paradox. For a much more detailed discussion on the Twin Paradox see the article in this Wiki on the Twin Paradox.

The net result of the debate showed that interpreting special relativity’s time dilation as causing a physical effect such as a slowing of proper time accumulation inherently led to contradictions. Hence, the logical conclusion was that special relativity’s time dilation needed to be seen as limited to describing “just observed” effects (i.e., both observers observe the other’s clock to be running slow without there being any necessary implication about relative proper time accumulation rates).

Logic Problem For Time Dilation Describing Proper Time

Let us have clocks at rest in two inertial frames A and B which are moving at relative velocity v relative to each other. Using the interpretation of special relativity time dilation that says clocks run slow (i.e., accumulate proper time more slowly) as a function of their relative velocity with respect to each other, then, if we apply that interpretation consistently, special relativity says that clocks in A run slower than clocks in B AND clocks in B run slower than clocks in A. This is not merely “counterintuitive”, but rather it’s a logic contradiction.

Empirical Data

Instead of the empirical data supporting special relativity’s construct of time dilation, it instead supports Lorentz Relativity’s clock retardation which says that clocks will slow as a function of absolute velocity with respect to a single, preferred frame.

Relativists erroneously claim that the empirical data supports the interpretation of special relativity’s time dilation that describes symmetrically changing proper time accumulation rates - however, since that interpretation leads to logic contradictions, it is not a viable interpretation – in addition, much of the empirical data is also at odds with this interpretation. A discussion of the various categories of empirical data supporting clock retardation as a function of absolute velocity and how that data has been erroneously interpreted by relativists is discussed below.

Particle Accelerators

In both linear and circular particle accelerators, the half-life of particles has been shown to increase as a function of their increasing velocity with respect to a single, preferred frame, thus confirming Lorentz’s asymmetric clock retardation.

Relativists claim that the logically invalid interpretation of special relativity’s time dilation that describes symmetrically changing proper time accumulation rates has been confirmed. However, the data is analyzed from the point of view of a single frame – at CERN and most other accelerators, that single frame is the Earth Centered Inertial frame.

Muon Decay In The Atmosphere5

The earthbound observer sees muons created in the upper atmosphere as byproducts of high energy cosmic ray proton impacts with atomic nuclei. Due to the thickness of the atmosphere and the very short half-life of the muon, very few such muons would be expected to reach the earth's surface (only 1 in every 10138). However, a great quantity of muons do reach the earth and even penetrate 100s of meters into the earth. This experimental result is interpreted as proof of special relativity's (symmetric) time dilation, but this is not a logically consistent interpretation. It is also not mentioned by relativists that this empirical data directly supports the alternative, Lorentz Relativity’s clock retardation.

It's claimed by relativists that it’s special relativity’s time dilation, that gives the muon's "clock" much more time for the "high speed" muon to decay and that gives the muon more time to traverse the depth of the earth's atmosphere. To be consistent with special relativity, it is claimed that from the high speed muon's frame, it would appear that muons that are moving slowly with respect to the earth would be observed to have a much longer decay rate than the high speed muons. The fact that, according to special relativity, both sets of clocks experience time dilation with respect to inertial frames that have speeds very near to the other set of muons can allegedly be explained in terms of relative simultaneity and the different views of what's simultaneous with the event of muon creation in the upper atmosphere and the event of that muon reaching the earth.

However, since this phenomenon involves a threshold event, namely, the decay or non-decay of the muon, the phenomenon cannot be explained by relative simultaneity or in terms of special relativity - this is, in general, true of allegedly relative velocity dependent, physical effects that involves a threshold.

In the current case, either the muons are traveling at greater than the speed of light in the earth frame, which is not consistent with special relativity, or their half-life has been physically and asymmetrically extended between the event of being created in the upper atmosphere and the event of reaching the earth. The asymmetry is established NOT by the earth observer determining the time between the two events of muon creation and the muon reaching the earth and then concluding the muon's clock is running slow. Instead, the asymmetric slowing is based on two absolute facts. We note that the atmosphere is approximately 20km thick and since the maximum speed for the muon is at most c (299,792,458 meters per second), that means it would take approximately 700μs for the fastest muon to traverse the entire thickness of the atmosphere. However, the mean lifetime of a muon at rest is just 2.2μs so the "high speed" muon clocks must be slowed by a factor of at least 300 to reach the surface of the earth. (While we discuss the logic in terms of a single muon, it also holds when viewed as a statistical argument about a large set of muons. If we look at the set of all cosmic ray created muons heading toward the earth, we find that their "clocks" have to be physically slowed in order to account for the number of muons that actually do reach the earth's surface.)

Thus, the asymmetric physical slowing is established by using two absolute facts, namely, the upper limit speed of c (according to special relativity) and the fact that the muon successfully survived its trip from the upper atmosphere to the surface of the earth and perhaps beyond. This cannot be explained as a "just observed" phenomenon which is observer dependent. The survival of the muons and their reaching the surface of the earth is an absolute fact - an observer independent fact. The percentage of high atmosphere muons that reach the surface of the earth is an absolute fact - an observer independent fact. The velocity of cosmic ray produced muons relative to the earth's atmosphere must be less than c, according to special relativity. So the only way to avoid concluding that the high atmosphere muons' clocks don't physically, asymmetrically slow with respect to the muons that move slowly with respect to the earth is to claim that special relativity's length contraction means the atmosphere is physically, asymmetrically contracted - otherwise the muons won't physically survive the trip. In fact, Wikipedia and many relativists invoke this solution. Wikipedia says, "From the viewpoint (inertial frame) of the muon, on the other hand, it is the length contraction effect of special relativity which allows this penetration, since in the muon frame, its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame."

Unfortunately, this frame dependent approach about what’s observed doesn’t begin to address the observer independent argument about absolute facts regarding the threshold event of surviving (or not surviving) the passage through the earth’s atmosphere and reaching the earth. [Another example of how threshold events show that special relativity cannot be describing physical effects, as opposed to just observations, is given at the "Two Step Argument #2" page at TwinParadox.net.]

Thus, we see that muons created by cosmic ray collisions in the upper atmosphere reach the earth's surface because there is an absolute, asymmetric, physical slowing of those muons' clocks when compared to the clocks of muons that are moving slowly with respect to the ECI frame. This asymmetric, physical slowing of clocks as a function of velocity with respect to the earth's frame cannot be explained by special relativity's constructs that are functions of (symmetric) relative velocity.

GPS

GPS uses a physical model built on physical asymmetric clock retardation as a function of velocity with respect to a unique frame, namely, the ECI (Earth Centered Inertial) frame.1 GPS uses the velocity of its satellite clocks with respect to the ECI frame and the velocity of earthbound clocks with respect to the ECI frame to determine how much each clock has slowed relative to a clock at rest in the ECI frame and then computes the ratio of those rates to compare the expected satellite clocks’ rates to the earth clock rates.1 As discussed above, even though one is using an equation that looks like special relativity’s time dilation and one is using velocity "relative" to the ECI frame, one is NOT actually using special relativity time dilation.

GPS uses the rotational velocity of the satellite clocks and the rotational velocity of the earthbound clocks relative to the (non-rotating) ECI frame and computes how much each set of clocks would slow relative to hypothetical clocks at rest in the ECI frame. Next, GPS uses those two ratios of the clocks relative to a 3rd party clock (the hypothetical clock at rest in the ECI frame) to compute the ratio of the satellite clock rate to the earthbound clock rate to determine the relative velocity effect.

This procedure is used not just for a complete orbit but for every part of the (non-circular) orbit as the rotational velocity varies so the methodology must work for each very small segment of the orbit to get the very high precision GPS applications require – particularly the newer applications. If special relativity could be used with GPS that would require that the high precision results could be obtained for each very small segment using any arbitrarily chosen inertial frame and not just limited to using a single, preferred frame, namely, the ECI frame.

However, it’s easy to show that special relativity cannot, in general, do that. As a purely hypothetical example selected for clarity of exposition of the concept, consider two satellite clocks A & B together at rest, but then A & B start moving in orbits of opposite direction at rotational velocity v with respect to the ECI frame. Let’s examine the situation of a very small segment centered at point X where clocks for A & B & ECI are arbitrarily close. ECI would see both A and B moving away from itself with (tangential) velocity v (albeit in opposite directions). So ECI would compute that both clocks slowed down with respect to the ECI clock by the same amount and, hence, would conclude that the two clocks, A & B, had the same rate. Let’s now use special relativity with another inertial frame D which has the same velocity as the A clock at point X when Clock A and B pass arbitrarily close to each other at point X. Then the time dilation calculations using the inertial D frame would be quite different than for the ECI frame as it would calculate that the B clock rate was much, much slower than the A clock rate. [As an aside, let’s look at small enough segments of clock A’s & clock B’s orbits that we can say, as relativists often do, that clock A & clock B approximate being in an inertial frame near enough for special relativity and then for the two examples given above we have, using special relativity, inertial frame A and inertial frame B giving contradictory results about time dilation not only with each other but also with the ECI frame and with frame D.]

Hence, trying to use special relativity’s relative velocity conruct would not only, in general, give the wrong answer for GPS, but it would also give multiple, contradictory answers depending on which inertial frame one chose to use as the base for calculations. All of this is straightforward and readily understandable to anyone not wedded to special relativity, yet it goes unheeded. As is the case with many new ideas in science, it can take a very long time to accept. Despite well-meaning claims to the contrary, GPS does not use the special relativity physics model, but instead uses the construct of velocity with respect to a single, preferred frame – this has been confirmed by GPS designers and consultants who have focused on this issue(Ron Hatch & Van Flandern References).

Observations from particle accelerators and atmospheric muons reaching the earth just give data gathered from one frame, the ECI frame, and do NOT give data from the “moving” particle perspective. As such, these sources do not directly address the issue of whether time dilation is symmetric (i.e., “just observed”) or asymmetric (i.e., physical). GPS data shows that time dilation (or rather clock retardation) is unquestionably asymmetric and physical – absolute velocity does affect clock rate.

In addition to the above, the GPS data shows that both the asymmetric physical proper time accumulation rate of atomic clocks and the observed rate are NOT, in general, dependent on relative velocity, but instead are dependent on their individual absolute velocities with respect to a single, preferred frame.

Hafele-Keating Experiment

The Hafele-Keating experiment, which was conducted prior to the GPS system being implemented, compares the proper time accumulation rates of atomic clocks at rest on the surface of the earth with the rates of airborne atomic clocks that were flown around the earth - some in an easterly direction and some in a westerly direction. As such, it mimics the time dilation physics of GPS and is subject to all the comments above regarding GPS.

What’s the Official Academic Position on Special Relativity’s Time Dilation?

First, as stated above, the de facto, non-official position, obtained by reading physics textbooks and physics journals and by seeing what’s taught in physics classrooms of leading colleges and universities, is that both, mutually exclusive interpretations of special relativity’s time dilation described above are held to be valid.

To resolve that dilemma, a number of German scientists have put in multiple requests to get the official interpretation of special relativity’s time dilation from the Albert Einstein Institute (AEI) in Germany. The AEI has been designated by the German government as the official spokes-organization on relativity and, by law, is supposed to answer such questions. The AEI has continually refused to give an official interpretation of special relativity’s time dilation – presumably because they are aware that any of three possible answers supporting special relativity will prove to be problematic.

Summary

In recent decades, high precision GPS data has shown that neither relativist interpretation of special relativity’s time dilation is correct. Instead, both the observed and actual clock rate is a function of absolute velocity relative to a single, preferred frame which, in the vicinity of the earth is, at least approximately, the Earth Centered Inertial (ECI) frame. Such findings are consistent with all prior empirical data.

However, since physics academia remains convinced that special relativity is correct, most relativists explicitly or implicitly espouse both the “just observed” AND the asymmetric, physical effect interpretations of special relativity’s time dilation even though they are mutually exclusive and both have been disproved by the empirical data and the physical interpretation has been shown to have fatal logic flaws.

It is hoped that some of today’s physics students will avail themselves of the thousands of publications based on critical thinking on special relativity’s time dilation and on special relativity itself [3] so that progress can be made in the future in the areas of spacetime physics and its use in associated disciplines such as astronomy and cosmology